Archive for the 'Bond Dissociation Energy' Category

A note here on a few recent Angew. Chem. articles of interest to readers of this blog. The first is a comment by Frenking1 concerning the “trilogue” by Shaik, Hoffmann and Rzepa2 which discusses the nature of C2, especially the notion that this molecules may possess a quadruple bond (see this post for a previous post on this article.) Frenking argues that the force constant associated with the C-C stretch in C2 is smaller than that in acetylene, so how can one argue that there is some quadruple bond character in C2? A reply from the original authors3 accompanies the comment by Frenking, and they respond by noting that the PES for bond stretching is unusually flat. I had the generally sense, though, that the authors of both articles were really talking past each other and that an opportunity for a more fruitful discussion has been missed.

The other article of note is an excellent review of de novo enzyme design as performed by the Baker and Houk labs.4 This review, authored by leaders of this effort, highlights their approach to this “holy grail” problem. The general notion is to use standard tools of computational chemistry to design a theozyme. Next, this theozyme is placed into known protein motifs with the attempt to have it fit without too much steric clash. The protein is then mutated one residue at a time to optimize the fit and binding of the theozyme to substrate. Lastly, the best targets are synthesized and tested. (The reader can see my post one of their projects: synthetic Diels-Alderase.)

A short note here mainly to call to the reader’s attention a fascinating “trialogue” on the C2 molecule.1 Shaik, Danovich, Wu, Su, Rzepa, and Hiberty2 recently presented a full CI study of C2 and concluded that the molecule contains a quadruple bond (see my previous post on this paper). This work was inspired in part by a blog post by Henry Rzepa.

The trialogue1 is a conversation between Sason Shaik, Henry Rzepa and Roald Hoffmann about the nature of C2, its 4th bond, its diradical character, and some historical detours to see how some of our theoretical chemistry ancestors came close to proposing a quadruple bond. The discussion weaves together simple MO pictures, simple VB models, and the need for much more sophisticated analysis to ultimately approach the truth. Very much worth pointing out is the careful analysis of trying to tease out bond dissociation energies, especially analyzing the assumptions made here – including the possibility of errors in the experiments and not just errors in the computations! This is a very enjoyable read, following these three theoreticians as they traipse about the complex C2 landscape!

Inspired by a blog post of Henry Rzepa (see here) Shaik and co-workers examined the C2 species with an eye towards the nature of the bond between the two carbon atoms.1 Using both a valence bond approach and a full CI approach, they end up at the same place: there is a quadruple bond here!

The argument rests largely on a definition of of an in situ bond energy. For the VB approach, this requires choosing as a reference a non-bonding interaction between the atoms with regards to a pair of electrons. For the CI approach, the bond energy is half the energy of the singlet-triplet gap. So, for C2, the VB/6-31G* estimate of the bond energy of the putative fourth bond is 14.3 kcal mol-1. For the full CI/6-31G* computations of the singlet-triplet gap, the bond energy estimate is 14.8 kcal mol-1, and using the experimental value of the gap, the estimate is 13.2 kcal mol-1. Not a strong bond, but certainly meaningful!

In the VB approach, the fourth bond is a weighted sum of the antibonding 2σu and bonding 3σg orbitals – a combination that gives rise to small constructive overlap between the two C atoms. In the CI model, the wavefunction is dominated by the first two configurations; the first configuration, with a coefficient of C0=0.828 has 2σu doubly occupied and the second coefficient, with CD=0.324, has the 3σg orbital doubly occupied. Considering that 3σg is a bonding orbital, the significant contribution of this configuration gives rise to the fourth bond.

InChIs

Shaik, Wu and Hiberty have proposed a third bond type, and they have a nice review article in Nature Chemistry.1 Along with the long-standing concepts of the covalent bond and the ionic bond, they add a third category: the charge-shift bond.

The valence bond wavefunction for the diatomic A-B is written as

Ψ(VB) = c1φcov(A-B) + c2φion(A+B–) + c3φion(A–X+)

Typically one of these terms dominates and we call the bond covalent if c1 is the largest coefficient or ionic if either c2 or c3 is the largest term. The bond dissociation energy (De) is the difference in energy of the total VB wavefunction (above) and the energy of the separate radicals A. and B.. One can determine the energy due to just a single component of the total VB wavefunction. One might expect that for a covalent bond, the bond dissociation energy derived from just the c1φcov(A-B) term would be close to De. For many covalent bonds this is true. However, Shaik and co-authors show a number of bonds where this is not true. For example, in the F-F bond, the covalent term is destabilizing. Rather, it is the resonance energy due to the mixing of the 3 VB terms that leads to bond formation. Shaik, Wu and Hiberty call this the “charge-shift bond”. They describe a number of examples of typically understood homonuclear and heteronuclear covalent bonds that are in fact charge-shift bonds, and an example of an ionic bond that really is charge-shift.

They argue that the charge-shift bond manifests as a consequence of the virial theorem. When an atom participates in a bond, its size gets smaller and this results in an increase in its kinetic energy. If the atom gets very small, then a substantial resultant change in the potential energy must occur, and this is the charge-shift bond. This also occurs in bonds involving atoms with many lone pairs; the lone-pair bond-weakening effect also causes a rise in kinetic energy that must be offset.

The authors speculate that many more examples of the charge-shift bond are waiting to be uncovered. It will be interesting if this concept catches hold and how quickly it will incorporated into general chemistry textbooks.

The bond dissociation energies (BDE) of the O-H bond of oximes R1R2C=N-OH) are discussed in Chapter 2.1.1.2. The controversy associated with these values originates from conflicting experimental data coming from calorimetric and electrochemical experiments. Some of the conflicting data are listed in Table 1. The electrochemical method provides energies at least a couple of kcal mol-1 too large, sometimes much more than that. I described in the book some composite method computations (G3MP, G3, CBS-QB3 and CBS-ANO)1 that suggest the BDE of acetone oxime is around 85 kcal mol-1, consistent with the calorimetric results. These authors could not apply these expensive methods to other compounds and were forced to use UB3LYP, which underestimates the values of the BDEs.

Fu6 has now applied the ONIOM-G3B37 approach to this problem. This is a clever way of attacking large molecules that require rather large computations to appropriately treat the quantum mechanics. So, each step of the G3B3 composite method is split into two levels: the high level is computed with the appropriate method from the G3B3 procedure, while the low level is treated with B3LYP. These resulting BDEs are listed in Table 1 and show remarkably nice agreement with the calorimetric results. These computed BDEs confirm that the electrochemical results are in error. Fu also computed the BDEs of some 30 other oximes for which electrochemical BDEs are available and for the large majority of these compounds, the electrochemical values are again too large.

In Chapter 2.2, we suggest that the experimental deprotonation energy (DPE) of cyclohexane is in doubt. G2MP2 predicts the DPE of cyclohexane is 414.5 kcal mol-1, a figure significantly higher than the experimental1 value of 404 kcal mol-1. Given that the deviation between the G2MP2 computed DPE and experiment is about 2 kcal mol-1, we suggest that cyclohexane should be re-examined.

In a recent JACS article,2 Kass calls into question the experimental bond dissociation energies (BDE) of the small cycloalkanes. With his experimental determination of the BDE of both the vinyl and allylic positions of cyclobutene, Kass can compare experimental and computed BDEs for a range of hydrocarbon environments, as listed in Table 1. The two composite methods G3 and W1 provide excellent BDE values for the small alkanes, one acyclic alkene, and the small cyclic alkenes. These composite methods appear to accurately predict BDEs of hydrocarbons.

However, the small cyclic alkanes are dramatic outliers. The well-accepted experimental BDEs of cyclopropane, cyclobutane, and cyclohexane are 3-5 kcal mol-1 lower than those predicted by the composite methods. Given the strong performance of the computational methods, and the difficulties associated with experimental determinations of BDEs, Kass suggests that the BDEs of these cycloalkanes are in error. Further experiments are deserved.